Most computer based animation systems use function curves to model how the value of an animated variable is modified over time. Function curves editors have been based on either functional splines or parametric splines.
Examples of splines include Bezier, Cardinal, B-Spline or Hermite. All of these splines can be either functional or parametric. A functional cubic Bezier spline is defined by a piecewise function made of cubic polynomials and a parametric cubic Bezier spline is defined by a set of parametric cubic curves. In order to define a function, a parametric spline must have one of its components, e.g. the X component, always increasing with respect to the parameter.
It is theoretically possible to achieve the same curve shape by the two methods. However, functional splines requires a much larger number of points for defining the function curve than the number required for parametric splines. As a result, users view parametric function curves as giving more and easier control on the animation.
In both systems, the editing process starts by the user creating a number of keys on a function curve. A key is a time and value pair defined by the user. A function curve is thus an ordered set of function curve segments separated by keys. When the user wants to modify the shape of a function curve segment between two keys, new intermediate keys can be added that better approximate the desired shape and therefore augment the number of segments. Additionally, other controls that modify the curve segment shape can be used.
The function curve editor used in SOFTIMAGE 3D v3.5 is based on functional splines. The function curve F is a piecewise polynomial function of t, time. At each key which is used to define the function F, a tangent is provided for the user to manipulate. The user can only modify the direction of the tangent. The tangent length cannot be modified because it is fixed when using functional polynomial splines.
Functional splines have only two degrees of freedom, the tangent direction at both ends, for controlling the function curve shape between two keys. In contrast, parametric splines has four degrees of freedom, the tangent direction and the tangent length at both ends. Therefore, the set of curve shape that can be reached by the former system is much smaller than the set that can be reached by the latter.
The function curve editor used in the Particle module of SOFTIMAGE 3D v3.51 is based on parametric splines. A tangent is provided for modifying the slope of the spline at the key. The user edits a curve segment by dragging key tangent handles, controlling the tangent angle and the tangent length. However, if the new tangent defines a new parametric curve segment which is not monotonic in the X direction, unusable pieces of the curve segment are highlighted or signalled to the user who must then modify the tangents so that the curve segment verifies the monotonicity condition.